no 



SCIENCE 



[N. S. Vol. XLI. No. 1047 



others, greatly needs the help that the 

 mathematician can give. On the other 

 hand, I believe that the mathematician has 

 something to learn from the astronomer 

 with regard to the point of view from which 

 he pursues his researches. The difference 

 in this respect between the two is becoming 

 greater and greater. In choosing a subject 

 for an address this afternoon, I thought 

 it best to take advantage of one of the rare 

 opportunities that an astronomer as such 

 gains audience with the mathematicians, 

 and to dwell upon this difference of view- 

 point, with the hope of aiding in bringing 

 together those who have meat and can not 

 eat, and those who would eat but want it. 

 Any such attempt, however ineffective by 

 itself and however feeble in itself, is well 

 worth while. 



This difference in view-point is nothing 

 more than a recurrence of the struggle that 

 occurs in every kind of human activity be- 

 tween the essentials of a subject and the 

 technique of that subject. It is a remark- 

 able fact that the outcome of this struggle 

 is not always in favor of the former, but 

 that mere technique is sometimes able to 

 gain permanent mastery and to submerge 

 completely the objects for which it was 

 created. The best illustration of this is 

 to be found in the painter's art. "We know 

 that there was a time when painting was 

 regarded as a mode of expression through 

 which lessons might be taught and learned, 

 or through which at least the world might 

 be amused. But for many a long day 

 painters have refused to take this view of 

 their art. They hold in frank contempt a 

 picture that tells a story, and their stand- 

 ards of what constitutes a great picture are 

 unintelligible to any one who is not him- 

 self a painter. You will remember the pic- 

 ture by Whistler, at the Metropolitan Mu- 

 seum of Art in New York, called "A Wo- 

 man in White." Although executed in 



oils, it is wholly in black and white. We 

 are told that it was painted to show that 

 certain effects could be produced in oils 

 without the use of color. Here then is a 

 painting that artists deem a great one, al- 

 though to the general public it has no sub- 

 ject at all and conveys next to nothing. 

 The majority of modern paintings belong 

 to the same class and it has gotten to be 

 well understood that artists are to paint 

 only for other artists. In any definition 

 of a great painting, skill and technique are 

 indispensable, but a man is at once called a 

 Philistine if he asks that artists use their 

 talents for some other purpose than merely 

 to record and exhibit personal achievement. 



Painting and poetry are arts that in 

 their essentials are much the same, their 

 chief difference being one of tools. But 

 while the painter has glorified his tools 

 more and more, the poet has kept his head, 

 and has not forgotten what tools are for. I 

 suppose it would be possible to construct a 

 poem without using any other vowels than 

 o and u. If so we should have the literary 

 counterpart of Whistler's "Woman in 

 White." Of course such an effort would 

 not be regarded seriously for a moment, 

 nor should we tolerate in literature any 

 mere exhibition of technique. Yet tech- 

 nique is quite as indispensable here as in 

 painting, and great facility is as rare in the 

 one art as in the other. 



Astronomy and mathematics have their 

 technique and are having their struggle 

 with it. A century ago Gauss, a great 

 mathematician and a great astronomer, 

 speaking for his times as much as for him- 

 self, announced as his motto, "Pauca sed 

 matura," and adopted as his crest a tree 

 laden with fruit, few in number but re- 

 markable for their perfection. Such senti- 

 ments as these and the feeling that lay be- 

 hind them have undoubtedly done more to 

 hinder the progress of science than to ad- 



